Stefano Fronzoni

PhD Candidate

Mathematical Institute, University of Oxford

About me

I am a DPhil student in Applied Mathematics at University of Oxford. My main interest is Numerical Analysis and Computational Mathematics. I am focused on the development of efficient algorithms to solve partial differential equations and optimisation problems.

Education

  • University of Oxford (2022-present)

    PhD in Mathematics

  • University of Trento (2020-2022)

    Master's Degree in Mathematics

  • Durham University (2019-2020)

    Erasmus Exchange Programme

  • University of Bologna (2016-2020)

    Bachelor's Degree in Mathematics

Interests

  • Numerical Analysis

  • Scientific Computing

  • Modeling and Simulation

  • Optimisation

  • Numerical methods for PDEs

Publications

∙ A finite-volume scheme for fractional diffusion on bounded domains ∙
arXiv: 2309.08283

We propose a new fractional Laplacian for bounded domains, expressed as a conservation law and thus particularly suited to finite-volume schemes. Our approach permits the direct prescription of no-flux boundary conditions. We first show the well-posedness theory for the fractional heat equation. We also develop a numerical scheme, which correctly captures the action of the fractional Laplacian and its anomalous diffusion effect. We benchmark numerical solutions for the L'evy-Fokker-Planck equation against known analytical solutions. We conclude by numerically exploring properties of these equations with respect to their stationary states and long-time asymptotics.


Conferences

Heidelberg Laureate Forum ∙ Heidelberg, Germany, 2023

Numerical Aspects of Hyperbolic Balance Laws ∙ Cortona, Italy, 2023

SIBBM Frontiers in Molecular Biology ∙ Italy, 2021